Question

In Exercises 3–8, let A, B, C, D, ... , Z points in $R^3$. Simplify the given quantity.

role="math" localid="1663305734277" $\overrightarrow{BD}-\overrightarrow{CD}$

Short answer

$\overrightarrow{BD}-\overrightarrow{CD}=\overrightarrow{BC}$

Step-by-step solution

Given

$\overrightarrow{BD}-\overrightarrow{CD}$

Simplify

As we know, taking the negative of any vector will change the direction of that vector.

$-\overrightarrow{CD}=\overrightarrow{DC}$

$$\begin{gathered} \overrightarrow{BD}-\overrightarrow{CD}=\overrightarrow{BD}+\overrightarrow{DC} \\ =\overrightarrow{BC} \end{gathered}$$